Abstract
The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as well as arithmetic information about the associated reciprocal classes of binary quadratic forms. One striking feature is the absence of a gap beyond zero in the limiting distribution, contrasting with the analog Euclidean situation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 999-1035 |
| Number of pages | 37 |
| Journal | Algebra and Number Theory |
| Volume | 8 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2014 |
Keywords
- Hyperbolic lattice angles
- Hyperbolic lattice points
- Modular surface
- Pair correlation
- Reciprocal geodesics
ASJC Scopus subject areas
- Algebra and Number Theory